Similarity solution for linear counter-current spontaneous imbibition

Li, Y.; Morrow, Norman R.; Ruth, Douglas

doi:10.1016/s0920-4105(03)00071-8

Cited by 65 publications

(69 citation statements)

References 11 publications

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“…This corresponds to "co-current flow" and q w = q n . The opposite case is "counter-current flow", the mass-flow of the expelled liquid takes place in the exactly opposite direction from the invading one: q w = −q n [196]. In both cases, if the geometric setup allows for a one-dimensional equation we arrive at the effective diffusion equation…”

Section: Dynamical Saturationmentioning

confidence: 99%

Imbibition in disordered media

Alava

Dubé

Rost

2004

Advances in Physics

285

333

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The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this field. The emphasis is on an interfacial description, akin to the focus of a statistical physics approach. Coarse-grained equations of motion have been recently presented in the literature. These contain terms that take into account the pertinent features of imbibition: non-locality and the quenched noise that arises from the random environment, fluctuations of the fluid flow and capillary forces. The theoretical progress has highlighted the presence of intrinsic length-scales that invalidate scale invariance often assumed to be present in kinetic roughening processes such as that of a two-phase boundary in liquid penetration. Another important fact is that the macroscopic fluid flow, the kinetic roughening properties, and the effective noise in the problem are all coupled. Many possible deviations from simple scaling behaviour exist, and we outline the experimental evidence. Finally, prospects for further work, both theoretical and experimental, are discussed.

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Section: Dynamical Saturationmentioning

confidence: 99%

Imbibition in disordered media

Alava

Dubé

Rost

2004

Advances in Physics

285

333

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“…3.7d). The presence of the linear portions confirms that countercurrent imbibition is the dominant oil recovery mechanism (Li et al, 2003;Li et al, 2004). Close correlation between the TEO and OEO cases shows that the middle of the core acts as the no-flow boundary for the TEO core.…”

Section: Fit Of Aronofsky Et Al (1958) Equation To Scaled Spontaneoumentioning

confidence: 67%

Wettability and Oil Recovery by Imbibition and Viscous Displacement from Fractured and Heterogeneous Carbonates

Morrow¹,

Buckley²

2006

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About one-half of U.S. oil reserves are held in carbonate formations. The remaining oil in carbonate reservoirs is regarded as the major domestic target for improved oil recovery. Carbonate reservoirs are often fractured and have great complexity even at the core scale. Formation evaluation and prediction is often subject to great uncertainty. This study addresses quantification of crude oil/brine/rock interactions and the impact of reservoir heterogeneity on oil recovery by spontaneous imbibition and viscous displacement from pore to field scale.Wettability-alteration characteristics of crude oils were measured at calcite and dolomite surfaces and related to the properties of the crude oils through asphaltene content, acid and base numbers, and refractive index. Oil recovery was investigated for a selection of limestones and dolomites that cover over three orders of magnitude in permeability and a factor of four variation in porosity. Wettability control was achieved by adsorption from crude oils obtained from producing carbonate reservoirs. The induced wettability states were compared with those measured for reservoir cores. The prepared cores were used to investigate oil recovery by spontaneous imbibition and viscous displacement. The results of imbibition tests were used in wettability characterization and to develop mass transfer functions for application in reservoir simulation of fractured carbonates. Studies of viscous displacement in carbonates focused on the unexpected but repeatedly observed sensitivity of oil recovery to injection rate. The main variables were pore structure, mobility ratio, and wettability. The potential for improved oil recovery from rate-sensitive carbonate reservoirs by increased injection pressure, increased injectivity, decreased well spacing or reduction of interfacial tension was evaluated. Table A2. Contact angles on cleaved calcite after aging in crude oil (initially dry or wet with the same aqueous phase as that used to float off bulk oil)…………………………53 Table 2.1 Synthetic brine composition…………………………………………………..87 Table 2.2 Selected properties of crude oil samples………………………………………87 Table 2.3 Gambier and Edwards (GC) cores tested for the effect of initial water saturation. Table 2.4 Edwards (GC) cores tested for the effect of aging time for Cottonwood crude oil………………………………………………………………………………………...88 Table 2.5 Gambier and Edwards (GC) MXW-F cores tested for wetting stability and the effect of oil phase viscosity …………………………………………………………89 Table 3.1 Synthetic brine composition…………………………………………………104 Table 3.2 Edwards (GC) cores tested with different mineral oil viscosities…………...105 Table 3.3 Edwards (GC) cores tested for the effect of variation in core length (µ o = 3.8cP). Fig. 1.10 AFM image of calcite exposed first to (0.1M NaCl) brine then aged for 2 days and 21 days in E-1XD-00 crude oil (deflection image in water)………………………..37 Fig. 1.11 AFM image of calcite exposed first to (0.1M NaCl) brine then aged for 2 days and 21 days in Tensleep crude oil (deflection image...

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“…showing that the distance that the front advances is proportional to √ t, a well-known result for the situation, in the absence of gravity, before a dispersed front has reached the end of a core (Washburn 1921; Reis and Cil 1993;Li et al 2003;Tavassoli et al 2005). The time, t end , taken for the front to reach the end of the core at distance L max is…”

Section: Linear Imbibitionmentioning

confidence: 91%

Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

et al. 2008

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Counter-current imbibition occurs when brine spontaneously displaces oil from a very strongly water-wet rock. Experiments are usually carried out on cylindrical core plugs which have all of their faces open, mainly because this is easiest to do and also because it appears to give the most reproducible results. The flow patterns are complex, but a reasonable approximation can be obtained by assuming piston-like advance of fronts from the radial outer face and both flat ends. This separates the flow pattern into two types: linear imbibition into cones and radial imbibition into the surrounding toroid ring. Production versus time curves have been calculated for cylinders of varying aspect ratios and other core shapes. The analytical results confirm the experimental observation that sample shape does not have much effect on the shape of the production versus time curves. Bearing in mind the inherent variability of experimental results for individual core samples, the differences would be difficult to detect in experiments. The time for imbibition to be completed scales as the characteristic length. The function given by Ma et al. (J Pet Sci Eng 18:165-178, 1997) requires only a small correction factor for agreement with the analytical result. The present analysis makes straightforward the comparison of results from the complex flow condition 123 200 G. Mason et al. of all-faces-open imbibition with results from linear and radial experiments. A comparison is made with published results. Nomenclature a L toroid − L cone (m) A Area (m 2 ) A f Area of the displacement front (m 2 ) A i Area open to imbibition in the ith direction (m 2 ) A R Area of the cylinder at a general radius, R(m 2 ) b L cone /R max C spread Factor determined by the breadth and shape of the pore size distribution d Core diameter (m) f Fraction of the core filled K Permeability (m 2 ) k rnw Relative permeability of the non-wetting phase k rw Relative permeability of the wetting phase L c Characteristic length (m) L cone Length of a cone (m) L core Core length (m) L c,Ma Characteristic length calculated from Ma's equation (m) L f Distance from the open face to the front for the cone (m) L max Length of the core for linear imbibition (m) L toroid Length of the toroid (m) M Mobility factor (Pa −1 s −1 )n Total number of surfaces open to imbibition P c Capillary pressure (Pa) P cf Capillary pressure at the imbibition front (Pa) P co Capillary pressure at the open face (Pa) P nw Pressure in the non-wetting phase (Pa) P w Pressure in the wetting phase (Pa) q nw Flow of non-wetting phase (m 3 /s) q w Flow of wetting phase (m 3 /s) q R w Flow passing through the surface of the cylinder, radius R (m 3 /s) R f Radial distance of the front from the axis (m) R end Radius of the final position of the front for the shorter toroid (m) R core Core radius (m) R sphere Radius of spherical core (m) S wf Wetting phase saturation behind the front S wi Initial wetting phase saturation t Time (s) t D Dimensionless time t end Time when imbibition ceases (s) t f Time when ...

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Similarity solution for linear counter-current spontaneous imbibition

Cited by 65 publications

References 11 publications

Imbibition in disordered media

Imbibition in disordered media

Wettability and Oil Recovery by Imbibition and Viscous Displacement from Fractured and Heterogeneous Carbonates

Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

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